x->0 (sin[x])/x

phymatter

does lim _x->0 (sin[x])/x exist ? if yes then what is it , iguess 0 , but cannot figure out the reason .. pl. help...
note: [x] is greatest integer less than or equal to x

tiny-tim

hi phymatter!

Quote by phymatter

does lim _x->0 (sin[x])/x exist ? if yes then what is it , iguess 0

yes

(just choose your delta to be 0.9, whatever your epsilon

)

mathman

If-1 < x < 0, [x] = -1, if 0 < x < 1, [x] = 0. As a result , for x < 0, the limit is -∞ while for x > 0, the limit is 0.

TylerH

Quote by phymatter

note: [x] is greatest integer less than or equal to x

It's usually called the "floor" function.

I don't think it would exist. lim(x->0+) sin(floor(x))/x = 0 and lim(x->0-) sin(floor(x))/x = ∞. For there to be a limit, lim(x->0+) sin(floor(x))/x and lim(x->0-) sin(floor(x))/x must be equal, they're not.

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phymatter	x->0 (sin[x])/x does lim _x->0 (sin[x])/x exist ? if yes then what is it , iguess 0 , but cannot figure out the reason .. pl. help... note: [x] is greatest integer less than or equal to x

mathman Recognitions: Science Advisor	If-1 < x < 0, [x] = -1, if 0 < x < 1, [x] = 0. As a result , for x < 0, the limit is -∞ while for x > 0, the limit is 0.